Problems on Stewart formula and inequalities for the areas of the bisection planes of the dihedral angles of a simplex are studied with the theory and method of distance geometry. Stewart formula and some inequalities...Problems on Stewart formula and inequalities for the areas of the bisection planes of the dihedral angles of a simplex are studied with the theory and method of distance geometry. Stewart formula and some inequalities for the areas of the bisection planes of the dihedral angles of a simplex in nE are established.展开更多
In recent years, intensifying waterlogging, salt water intrusion, wetland loss, and ecosystem degradation in Chinese delta cities and adjacent regions have generated the pressing need to create an urban form that is s...In recent years, intensifying waterlogging, salt water intrusion, wetland loss, and ecosystem degradation in Chinese delta cities and adjacent regions have generated the pressing need to create an urban form that is suited to both current and future climates incorporating sea level rise. However, adaptation planning uptake is slow. This is particularly unfortunate because patterns of urban form interact with mean sea level rise （MSLR） in ways that reduce or intensify its impact. There are currently two main barriers that are significant in arresting the implementation of adaptation planning with reference to the MSLR projections composed of geomorphologic MSLR projections and eustatic MSLR projections from global climate warming, and making a comprehensive risk assessment of MSLR projections. The present review shows recent progresses in mapping MSLR projections and their risk assessment approaches on Chinese delta cities, and then a perspective of adapting these cities to MSLR projections as following six aspects. 1） The geomorphologic MSLR projections are contributed by the natural tectonic subsidence projections and the MSLR projections by anthropogenic geomorphologic change. The former needs to be updated in a global framework. The latter is accumulated by land subsidence from underground water depletion, water level fall caused by the erosion of riverbeds from a sediment supply decline attributed to the construction of watershed dams, artificial sand excavation, water level raise by engineering projects including land reclamation, deep waterway regulation, and fresh water reservoirs. 2） Controlling MSLR projections by anthropogenic geomorphologic changes. 3） The IPCC AR5 RCPs MSLRs scenarios are expected to be projected to the local eustatic MSLR projections on the Chinese deltas. 4） The MSLR projections need to be matched to a local elevation datum. 5） Modeling approaches of regional river-sea numerical with semi- analytical hydrodynamics, estuarine channel network, system dynamics and adaptation points are perspective. 6） Adaptation planning to MSLR projections requires a comprehensive risk assessment of the risk of flood, fresh water supply shortage, coastal erosion, wetland loss, siltation of ports and waterway in Chinese delta cities and adjacent regions.展开更多
During range-based self-localization of Wireless Sensor Network (WSN) nodes, the number and placement methods of beacon nodes have a great influence on the accuracy of localization. This paper proves a theorem which d...During range-based self-localization of Wireless Sensor Network (WSN) nodes, the number and placement methods of beacon nodes have a great influence on the accuracy of localization. This paper proves a theorem which describes the relationship between the placement of beacon nodes and whether the node can be located in 3D indoor environment. In fact, as the highest locating accuracy can be acquired when the beacon nodes form one or more equilateral triangles in 2D plane, we generalizes this conclusion to 3D space, and proposes a beacon nodes selection algorithm based on the minimum condition number to get the higher locating accuracy, which can minimize the influence of distance measurement error. Simulation results show that the algorithm is effective and feasible.展开更多
A metal-organic framework （MOF） has been obtained by using a linker extension strategy. Three di-anions of 4-（3,5-dimethyl- 1H-pyrazol-4-yl）-benzoic acid coordinate to three Cu（I） ions forming an extended trigon...A metal-organic framework （MOF） has been obtained by using a linker extension strategy. Three di-anions of 4-（3,5-dimethyl- 1H-pyrazol-4-yl）-benzoic acid coordinate to three Cu（I） ions forming an extended trigonal planar ligand, which links three di-copper paddlewheel units giving rise to a Pt304 net.展开更多
It is known that every triangle-free plane graph is 3-colorable.However,such a triangle-free plane graph may not be 3-choosable.In this paper,we prove that a triangle-free plane graph is 3-choosable if no 4-cycle in i...It is known that every triangle-free plane graph is 3-colorable.However,such a triangle-free plane graph may not be 3-choosable.In this paper,we prove that a triangle-free plane graph is 3-choosable if no 4-cycle in it is adjacent to a 4-or a 5-cycle.This improves some known results in this direction.展开更多
The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,...The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,9] and the eccentricity e ∈ [0,1）.In this paper we use Maslov-type index to study the stability of these solutions and prove that the elliptic Lagrangian solutions is hyperbolic for β ＆gt; 8 with any eccentricity.展开更多
基金Funded by the Natural Science Foundation of Anhui (2004kj104).
文摘Problems on Stewart formula and inequalities for the areas of the bisection planes of the dihedral angles of a simplex are studied with the theory and method of distance geometry. Stewart formula and some inequalities for the areas of the bisection planes of the dihedral angles of a simplex in nE are established.
基金Acknowledgments This study was financially supported by the Shanghai Science and Technology Committee （10dz1210600）, the National Sea Welfare Project （201005019-09）, the Natural Science Foundation of China （41476075, 41340044）, and the China Geological Survey （12120115043101 ）.
文摘In recent years, intensifying waterlogging, salt water intrusion, wetland loss, and ecosystem degradation in Chinese delta cities and adjacent regions have generated the pressing need to create an urban form that is suited to both current and future climates incorporating sea level rise. However, adaptation planning uptake is slow. This is particularly unfortunate because patterns of urban form interact with mean sea level rise （MSLR） in ways that reduce or intensify its impact. There are currently two main barriers that are significant in arresting the implementation of adaptation planning with reference to the MSLR projections composed of geomorphologic MSLR projections and eustatic MSLR projections from global climate warming, and making a comprehensive risk assessment of MSLR projections. The present review shows recent progresses in mapping MSLR projections and their risk assessment approaches on Chinese delta cities, and then a perspective of adapting these cities to MSLR projections as following six aspects. 1） The geomorphologic MSLR projections are contributed by the natural tectonic subsidence projections and the MSLR projections by anthropogenic geomorphologic change. The former needs to be updated in a global framework. The latter is accumulated by land subsidence from underground water depletion, water level fall caused by the erosion of riverbeds from a sediment supply decline attributed to the construction of watershed dams, artificial sand excavation, water level raise by engineering projects including land reclamation, deep waterway regulation, and fresh water reservoirs. 2） Controlling MSLR projections by anthropogenic geomorphologic changes. 3） The IPCC AR5 RCPs MSLRs scenarios are expected to be projected to the local eustatic MSLR projections on the Chinese deltas. 4） The MSLR projections need to be matched to a local elevation datum. 5） Modeling approaches of regional river-sea numerical with semi- analytical hydrodynamics, estuarine channel network, system dynamics and adaptation points are perspective. 6） Adaptation planning to MSLR projections requires a comprehensive risk assessment of the risk of flood, fresh water supply shortage, coastal erosion, wetland loss, siltation of ports and waterway in Chinese delta cities and adjacent regions.
基金Supported by the National Natural Science Foundation of China (No.61003236 61171053)+2 种基金the Doctoral Fund of Ministry of Education of China (No.20113223110002)the Natural Science Major Program for Colleges and Universities in Jiangsu Province (No.11KJA520001)Science & Technology Innovation Fund for higher education institutions of Jiangsu Province (CXZZ12_0481)
文摘During range-based self-localization of Wireless Sensor Network (WSN) nodes, the number and placement methods of beacon nodes have a great influence on the accuracy of localization. This paper proves a theorem which describes the relationship between the placement of beacon nodes and whether the node can be located in 3D indoor environment. In fact, as the highest locating accuracy can be acquired when the beacon nodes form one or more equilateral triangles in 2D plane, we generalizes this conclusion to 3D space, and proposes a beacon nodes selection algorithm based on the minimum condition number to get the higher locating accuracy, which can minimize the influence of distance measurement error. Simulation results show that the algorithm is effective and feasible.
基金supported by the U.S. Department of Energy (DOE Grants DE-FC36-07GO17033)the Welch Foundation (A-1725)+1 种基金supported by the National Science Foundation/Department of Energy under grant number NSF/CHE-0822838supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357
文摘A metal-organic framework （MOF） has been obtained by using a linker extension strategy. Three di-anions of 4-（3,5-dimethyl- 1H-pyrazol-4-yl）-benzoic acid coordinate to three Cu（I） ions forming an extended trigonal planar ligand, which links three di-copper paddlewheel units giving rise to a Pt304 net.
基金supported by the Zhejiang Provincial Natural Science Foundation ofChina (Grant No. Y6090699)National Natural Science Foundation of China (Grant No. 10971198)ZhejiangInnovation Project (Grant No. T200905)
文摘It is known that every triangle-free plane graph is 3-colorable.However,such a triangle-free plane graph may not be 3-choosable.In this paper,we prove that a triangle-free plane graph is 3-choosable if no 4-cycle in it is adjacent to a 4-or a 5-cycle.This improves some known results in this direction.
基金supported by National Natural Science Foundation of China (Grant No.11131004)
文摘The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,9] and the eccentricity e ∈ [0,1）.In this paper we use Maslov-type index to study the stability of these solutions and prove that the elliptic Lagrangian solutions is hyperbolic for β ＆gt; 8 with any eccentricity.
